{"id":"https://openalex.org/W2125151663","doi":"https://doi.org/10.1145/2213977.2213995","title":"On identity testing of tensors, low-rank recovery and compressed sensing","display_name":"On identity testing of tensors, low-rank recovery and compressed sensing","publication_year":2012,"publication_date":"2012-05-19","ids":{"openalex":"https://openalex.org/W2125151663","doi":"https://doi.org/10.1145/2213977.2213995","mag":"2125151663"},"language":"en","primary_location":{"id":"doi:10.1145/2213977.2213995","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2213977.2213995","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-fourth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},"type":"article","indexed_in":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1111.0663","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Michael A. Forbes","orcid":null},"institutions":[{"id":"https://openalex.org/I4210110987","display_name":"IIT@MIT","ror":"https://ror.org/01wp8zh54","country_code":"US","type":"facility","lineage":["https://openalex.org/I30771326","https://openalex.org/I4210110987"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Michael A. Forbes","raw_affiliation_strings":["MIT, Cambridge, MA, USA"],"affiliations":[{"raw_affiliation_string":"MIT, Cambridge, MA, USA","institution_ids":["https://openalex.org/I4210110987"]}]},{"author_position":"last","author":{"id":null,"display_name":"Amir Shpilka","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Amir Shpilka","raw_affiliation_strings":["Technion --- Israel Institute of Technology, Haifa, Israel"],"affiliations":[{"raw_affiliation_string":"Technion --- Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I4210110987"],"apc_list":null,"apc_paid":null,"fwci":2.798,"has_fulltext":false,"cited_by_count":26,"citation_normalized_percentile":{"value":0.90341358,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"163","last_page":"172"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11778","display_name":"Electrical and Bioimpedance Tomography","score":0.9925000071525574,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/linear-subspace","display_name":"Linear subspace","score":0.6064000129699707},{"id":"https://openalex.org/keywords/rank","display_name":"Rank (graph theory)","score":0.5989000201225281},{"id":"https://openalex.org/keywords/identity","display_name":"Identity (music)","score":0.5669999718666077},{"id":"https://openalex.org/keywords/tensor","display_name":"Tensor (intrinsic definition)","score":0.5564000010490417},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5400000214576721},{"id":"https://openalex.org/keywords/compressed-sensing","display_name":"Compressed sensing","score":0.5385000109672546},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.532800018787384},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5098999738693237},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5056999921798706}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6541000008583069},{"id":"https://openalex.org/C12362212","wikidata":"https://www.wikidata.org/wiki/Q728435","display_name":"Linear subspace","level":2,"score":0.6064000129699707},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.5989000201225281},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.5669999718666077},{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5564000010490417},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5400000214576721},{"id":"https://openalex.org/C124851039","wikidata":"https://www.wikidata.org/wiki/Q2665459","display_name":"Compressed sensing","level":2,"score":0.5385000109672546},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.532800018787384},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5098999738693237},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5056999921798706},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.48080000281333923},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4643999934196472},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.45320001244544983},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.41600000858306885},{"id":"https://openalex.org/C134567657","wikidata":"https://www.wikidata.org/wiki/Q193794","display_name":"Identity matrix","level":3,"score":0.3695000112056732},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3359000086784363},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3310000002384186},{"id":"https://openalex.org/C77926391","wikidata":"https://www.wikidata.org/wiki/Q603880","display_name":"Finite field","level":2,"score":0.3303999900817871},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32839998602867126},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.32679998874664307},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.30630001425743103},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.29910001158714294},{"id":"https://openalex.org/C65682993","wikidata":"https://www.wikidata.org/wiki/Q1056451","display_name":"Reflection (computer programming)","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2687999904155731},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2678000032901764},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.25290000438690186},{"id":"https://openalex.org/C90199385","wikidata":"https://www.wikidata.org/wiki/Q6692777","display_name":"Low-rank approximation","level":3,"score":0.25060001015663147}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1145/2213977.2213995","is_oa":false,"landing_page_url":"https://doi.org/10.1145/2213977.2213995","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Proceedings of the forty-fourth annual ACM symposium on Theory of computing","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:1111.0663","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1111.0663","pdf_url":"https://arxiv.org/pdf/1111.0663","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.745.2801","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.745.2801","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://arxiv.org/pdf/1111.0663.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1111.0663","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1111.0663","pdf_url":"https://arxiv.org/pdf/1111.0663","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1503731768","https://openalex.org/W1529624360","https://openalex.org/W1539607073","https://openalex.org/W1877591169","https://openalex.org/W1967348711","https://openalex.org/W1993359877","https://openalex.org/W1998853590","https://openalex.org/W2026036943","https://openalex.org/W2026944800","https://openalex.org/W2035710094","https://openalex.org/W2050570613","https://openalex.org/W2051305477","https://openalex.org/W2056236392","https://openalex.org/W2087857477","https://openalex.org/W2091564680","https://openalex.org/W2095547380","https://openalex.org/W2097016139","https://openalex.org/W2106221905","https://openalex.org/W2118550318","https://openalex.org/W2121894367","https://openalex.org/W2128510017","https://openalex.org/W2134311784","https://openalex.org/W2134332047","https://openalex.org/W2137147213","https://openalex.org/W2148132824","https://openalex.org/W2162442687","https://openalex.org/W2162451874","https://openalex.org/W2166163936","https://openalex.org/W2168831133","https://openalex.org/W2171403864","https://openalex.org/W4213098650"],"related_works":[],"abstract_inverted_index":{"We":[0,46,77,103],"study":[1],"the":[2,70,94,108,120,140,197,205,220],"problem":[3,49],"of":[4,22,53,81,88,110,114,122,183,199,222],"obtaining":[5],"efficient,":[6,26],"deterministic,":[7,27,165],"black-box":[8,44],"polynomial":[9,29],"identity":[10,30],"testing":[11,31],"algorithms":[12],"for":[13,86,100],"depth-3":[14],"set-multilinear":[15],"circuits":[16,23],"(over":[17],"arbitrary":[18,101],"fields).":[19],"This":[20],"class":[21],"has":[24,40,74],"an":[25],"white-box":[28],"algorithm":[32],"(due":[33],"to":[34,107,131,155,210,234],"Raz":[35],"and":[36,92,196],"Shpilka":[37],"[36]),":[38],"but":[39],"no":[41,225],"known":[42,232],"such":[43,64,184],"algorithm.":[45],"recast":[47],"this":[48,149,235],"as":[50],"a":[51,55,133,178],"question":[52],"finding":[54],"low-dimensional":[56],"subspace":[57],"H,":[58],"spanned":[59],"by":[60],"rank":[61,145,161],"1":[62],"tensors,":[63],"that":[65,142,158,169],"any":[66],"non-zero":[67],"tensor":[68],"in":[69,119,192],"dual":[71],"space":[72],"ker(H)":[73],"high":[75],"rank.":[76],"obtain":[78,93],"explicit":[79,226],"constructions":[80,227],"essentially":[82,202],"optimal-size":[83],"hitting":[84,98],"sets":[85,99],"tensors":[87],"degree":[89],"2":[90],"(matrices),":[91],"first":[95],"quasi-polynomial":[96],"sized":[97],"tensors.":[102],"also":[104],"show":[105],"connections":[106],"task":[109],"performing":[111],"low-rank":[112],"recovery":[113,126],"matrices,":[115,214],"which":[116,187],"is":[117,144,201],"studied":[118],"field":[121,194],"compressed":[123],"sensing.":[124],"Low-rank":[125],"asks":[127],"(say,":[128],"over":[129],"R)":[130],"recover":[132],"matrix":[134],"M":[135,143,188],"from":[136,172,186],"few":[137],"measurements,":[138,168,185],"under":[139],"promise":[141],"\u2264":[146,162],"r.":[147],"In":[148],"work,":[150],"we":[151,176],"restrict":[152],"our":[153,223],"attention":[154],"recovering":[156],"matrices":[157],"are":[159,170],"exactly":[160],"r":[163],"using":[164],"non-adaptive,":[166],"linear":[167],"free":[171],"noise.":[173],"Over":[174],"R,":[175],"provide":[177],"set":[179],"(of":[180],"size":[181],"4nr)":[182],"can":[189,207],"be":[190,208,211],"recovered":[191],"O(rn2+r3n)":[193],"operations,":[195],"number":[198],"measurements":[200,206],"optimal.":[203],"Further,":[204],"taken":[209],"all":[212,216],"rank-1":[213],"or":[215],"sparse":[217],"matrices.":[218],"To":[219],"best":[221],"knowledge":[224],"with":[228],"those":[229],"properties":[230],"were":[231],"prior":[233],"work.":[236]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}